ARTICLE IX. 



EQII\ All NT UNIFORM LOADS. 



AN equivalent uniform load i> one which givefl I lie Same 

 stress as does a loading which is not uniform. For any 

 given standard loading, the equivalent uniform load is dif- 

 ferent for stresses whose influence lines differ. Since the 

 forms of influence lines are innumerable, a table of exact 

 equivalent uniform loads for all stresses is impracticable. 

 A table of equivalent uniform loads, however, for stresses 

 whose influence lines are triangular may be used with little 

 error in selecting equivalent uniform loads for stresses whose 

 influence lines are not triangular. It is, therefore, sufficient 

 for practical purposes to make tables of equivalent uniform 

 loads for a series of triangular influence lines. It may be 

 shown that the equivalent uniform load for any triangular 

 influence line is dependent entirely upon the intervals li 

 and k, and is independent of the ordinate h at the apex 

 of the influence line. Consider the triangular influence line 

 in Fig. Ib to be for any stress S. Let the ordinate below 

 C be any value h. If q equals the equivalent uniform load 

 covering li and k, 



or 



S = qA z , or q = j- (A 



The area of this influence line ua 



A, = \ (I, + h) = \ L (B) 



Furthermore, if the concentrated live loads have been 

 placed so as to give the maximum pier reaction between 

 two spans h and k, this same position of loading will give 

 maximum 5, if the influence line for S is a triangle with the 



54 



